A graphical model is a probabilistic model that expresses the conditional dependence structure between random variables. Graphical models use a graph-based representation to encode a complete distribution over a high-dimensional space [1]}. Commonly used graphical models include Bayesian networks, Markov Random Fields, and factor graphs.
fig:factorgraph gives an example of such a factor graph. Circles represent random variables and squares represent factors.
A factor graph is a graphical model widely used in SLAM problems. Denote \(\mathbf {X}=\lbrace X_1,\cdots ,X_n\rbrace \)  as the random variables. Denote \(\psi _a(X_{\lbrace a\rbrace })\)  as a factor among random variable in set \(\lbrace a\rbrace \) . The the joint probability can be expressed as a product of factors:
\(p(\mathbf {X}=x) \propto \prod _{a\in \mathcal {A}} \psi _a \left(X_{\lbrace a\rbrace }=x_{\lbrace a\rbrace } \right)\) 
